Pneumatic Transport of Granular Materials in an Inclined Conveying

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Pneumatic Transport of Granular Materials in an Inclined Conveying Pipe: Comparison of Computational Fluid Dynamics-Discrete Element Method (CFD-DEM), Electrical Capacitance Tomography (ECT), and Particle Image Velocimetry (PIV) Results Yan Zhang, Eldin Wee Chuan Lim, and Chi-Hwa Wang* Department of Chemical and Biomolecular Engineering, National UniVersity of Singapore, 4 Engineering DriVe 4, Singapore, 117576

This paper presents three flow patternssdispersed flow, reverse flow, and half-ring flowsin the post-bend region of a 45° inclined pneumatic conveying pipe. Solid concentration and velocity distribution were measured using electrical capacitance tomography (ECT), particle image velocimetry (PIV), and a high-speed camera. The axial velocity of particles and solid transverse motion in the pipe cross section were obtained using a modified cross-correlation method from the ECT data for the three flow patterns. The axial velocity profile over the pipe cross section was compared with data obtained from the PIV system. In particular, emphasis has been placed on the characterization of the reverse-flow pattern, where negative values of solid velocities were observed. By analyzing the images captured with the high-speed camera, three distinct regions in the solid phase of the reverse-flow regime may be discerned. A dense region with high solid concentration formed next to the bottom wall of the inclined conveying pipe, while a dilute region with a relatively low solid concentration formed near the center of the pipe. Reverse flow was observed to occur predominantly in the dense region and a transition region between the two. Finally, the dynamic forces acting on single particles were analyzed for the three flow patterns. This analysis showed that the phenomena of reverse-flow and half-ring flow structure formation may be attributed to the effects of electrostatics. This finding has also been validated with results of numerical simulations performed in the present study. 1. Introduction Pneumatic conveying systems are widely used for the transportation of granular material in various industries. Research work performed in this field can be categorized according to different geometries of the conveying section used in the transportation process. These include pneumatic conveying through horizontal, vertical, and inclined pipes and about a bend. Many studies have been conducted on gas-solid flow in horizontal and vertical pipes, whereas relatively fewer studies are available on solid transport in inclined pipes. These are mainly focused on pressure drop data through the conveying pipes. For example, Levy et al.1 developed an analytical model for gas-solid suspension flow through an inclined pipe section, which predicted the ratio of the total pressure drop in an inclined pipe to that of a horizontal pipe and agreed with the experimental data satisfactorily; Hirota et al.2 examined the effect of mechanical properties and the angle of an inclined pipe on the pressure drop for the pneumatic conveying of fine powders. Other studies of granular flow focused on the different flow patterns arising from different physical conditions and operating parameters imposed. Zhu et al.3 used computational fluid dynamics (CFD) simulations to investigate the pneumatic conveying of granular solids through an inclined pipe at different inclinations and reported results on the influence of model parameters, inclination angle, and feeding conditions on the flow patterns. Experiments have also been performed to study solid flow patterns in pneumatic conveying through vertical and inclined pipes and various flow patterns were observed.4 In their work, regimes such as eroding dune flow and flow over a settled * To whom correspondence should be addressed. Tel.: 65-65165079. Fax: 65-6779-1936. E-mail: [email protected].

layer were imaged using electrical capacitance tomography (ECT), and some flow regimes with downflow were observed visually. However, detailed analyses were not given. The study on downflow or reverse flow has not drawn much attention among researchers. Among the limited literature on this subject, most have concentrated on heat-transfer investigations in liquid systems. Mare´ et al.5 investigated the laminar flow of water in an inclined isothermal tube numerically and experimentally using three-dimensional elliptical model and particle image velocimetry (PIV), respectively, and concluded that the combination of the Reynolds number (Re), Grashof number, and Prandtl number determined the phenomena of reverse flow. The objective of this work was to study three flow patternss dispersed, reverse, and half-ring flowsobserved in a 45° inclined conveying pipe. The methods applied for capturing solid flow patterns and velocity profiles include ECT, PIV, and a highspeed camera. The study on flow patterns is a fundamental concept in pneumatic conveying systems and is helpful toward understanding real-life problems, which may arise during actual operations. The appearance of the variety of solid flow patterns observed in laboratory experiments or actual industrial operations are normally attributed to the physical conditions used. However, some peculiar clustering behaviors may not be accounted for purely by hydrodynamics effects alone, such as the formation of ring structures in vertical and inclined pneumatic conveying. This paper attempts to analyze such flow behaviors of solid particles in an inclined pneumatic conveying pipe through the consideration of the effects of electrostatic charge generation. This continues from previous research studies6 on the electrostatics of granular flow in horizontal and vertical pneumatic conveying systems and provides further

10.1021/ie061304i CCC: $37.00 © 2007 American Chemical Society Published on Web 05/11/2007

Ind. Eng. Chem. Res., Vol. 46, No. 19, 2007 6067

Figure 1. Schematic of the pneumatic conveying experiment facility. Legend: 1, air control valve; 2, dryers; 3, rotameter; 4, hopper; 5, solids feed valve; 6, rotary valve feeder; 7, feed control valve; 8, computer; 9, DAM; 10, ECT plane 1; 11, ECT plane 2; 12, plane of PIV measurements; 13, plane of measurements for the high-speed camera; 14, measurements for induced current; 15, measurements for particle charge; 16, pressure transducer sensor 1; and 17, pressure transducer sensor 2.

Table 1. Experimental Conditions parameter

value

air flow rate solids feed valve roll speed of rotary valve pipe material pipe diameter (inner) pipe thickness particles conveying style particle material particle size particle density

1600 L/min, 1100 L/min, 1000 L/min 75% opening 25 rpm poly(vinyl chloride), PVC 40.0 mm 5.0 mm cycle polypropylene, PP 2.80 mm 1123 kg/m3

insights into the relationship between solids flow behavior and electrostatic effects. 2. Experimental Section 2.1. Experimental Setup. The experimental facility, which was modified from a previous study4,7 and used to perform the measurements, is shown schematically in Figure 1; the experimental conditions are listed in Table 1. Air from the compressor was metered and sent to the rotary air lock feeder (General Resources Corp., Hopkins, MN), where it entrained the particles. The rotary feeder equipped with eight pockets and a vent at the body of the rotary valve, providing the passage of the air leakage, was operated at a fixed speed of 25 rpm. The test section consisted of two 4-cm-inner-diameter (ID) horizontal

pipes: one is positioned at a distance of 3.41 m, and the lower one is positioned at a distance of 4.12 m. A 45° inclined pipe (4-cm ID) was connected to the two horizontal pipes. The entire conveying loop was made of poly(vinyl chloride) (PVC) pipes. 2.2. Electrical Capacitance Tomography (ECT). ECT is a noninvasive technique for measuring and displaying the concentration distribution of a mixture of two dielectric fluids. In this experiment, two sets of 12-electrode (10 cm long) ECT sensors (labeled as “10” and “11” in Figure 1) were arranged on the inclined pipe at distances of 1.45 and 2.18 m from a bend connecting this inclined riser to a horizontal duct at the bottom. A data acquisition module (DAM) (Process Tomography, Wilmslow, Cheshire, U.K.) was connected to the ECT sensors to gather capacitance data. The ECT was sampled at 40 Hz, corresponding to a time period of 0.025 s for each frame. The resolution of each frame was 1024 (32 × 32) pixels. The ECT system was calibrated for the lower and upper permittivity bounds: air was used for the lower bound (with 0 as the reference value) and solids were used as the upper bound (with 1 as the reference value). By post-processing the ECT data at each instant of time t, using the simultaneous iterative reconstruction technique (SIRT) described by Su et al.,8 the particle concentration in each pixel of one plane, R(x,y,z,t), was obtained. Here, as shown in Figure 1 by the viewing section A-A, x and y denote Cartesian coordinates in the cross-sectional plane, made dimensionless using the pipe diameter as the characteristic length, and z is the

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Ind. Eng. Chem. Res., Vol. 46, No. 19, 2007

axial coordinate denoting the location of the ECT electrodes. The solid velocity can be calculated based on cross-correlation of twin plane data, which was described by Hua et al.,9 Rao et al.,7 and Zhu et al.4 The time-averaged particle concentration R j t was found by averaging R(x,y,z,t) over a time period T (30 s in this case):

R j t(x,y,z) )

1 T

∫0T R(x,y,z,t) dt

(1)

The instantaneous value of the cross-sectional average particle concentration, R j s(z,t), is defined as

R j s(z,t) )

1 A

∫∫ R(x,y,z,t) dx dy

(2)

and the time-averaged value of R j s(z,t) is denoted by 〈R〉(z):

〈R〉(z) )

1 T

∫0T Rjs(z,t) dt ≡ A1 ∫∫ Rj t(x,y,z) dx dy

(3)

The correlation coefficient, C(d), was then computed as

1 C(d) ) T

∫0

T

3. Numerical Method

(R j s(z1,t) - 〈R〉(z1)) (R j s(z2,t + d) - 〈R〉(z2)) dt (4)

Here, z1 and z2 refer to upstream and downstream planes, respectively; d denotes the delay time. The dominant pattern propagation velocity (V*) was estimated from V* ) L/D, where L ) z2 - z1 (L ) 2.18-1.45 ) 0.73 m in the current work), is the axial distance between the two ECT sensors and D is the value of d at which C(d) assumes the largest value. V* estimated in this manner is clearly based on cross-sectional averages. One can also define pixel-pixel cross-correlation function as

c(x,y,d) )

1 T

∫0T (R(x,y,z1,t) R j t(x,y,z1)) (R(x,y,z2,t + d) - R j t(x,y,z2)) dt (5)

The dominant pattern propagation velocity (V(x,y)) was estimated from eq 6:

V(x,y) )

L D(x,y)

direction perpendicular to the lightsheet and transmitted to the computer for processing. The cross-correlation yields the distance traveled by the granules in a small time interval (dT ) 50-58000 µs) from the first snapshot to the second and the velocity distribution of granules in the plane can be determined by dividing by the time interval. In this study, the variation of velocity in the axial direction of the 45° inclined pipe was measured. 2.4. Electrostatic Measurements. During the pneumatic conveying process, frictional contacts between the solid particles and pipe wall generate electrostatic charges. With proper pipe connections, current induced on the surface of the pipe wall can be measured as a function of time using a digital electrometer (ADVANTEST R8252, Tokyo, Japan). The measurement section is labeled “14” in Figure 1 while details of the measurement methods have been described previously by Yao et al.6 In addition, the particle charge density was measured using a Faraday cage at the horizontal segment6 (labeled “15” in Figure 1).

(6)

where D(x,y) is the value of d at which c(x,y,d) assumes the maximum value (for that x and y). One limitation of the classical cross-correlation method arises from a basic assumption that the particle motion between the sensors is parallel to the pipe axis, i.e., perpendicular to the sensor plane. However, the actual movements are quite complex, and the trajectories of particles do not remain parallel to the pipe axis. Thus, it is necessary to introduce a new method,10 namely, the best-correlated pixel method, which does not require the assumption about the solid trajectories within a sensor volume and will be shown in section 4.1.1. 2.3. Particle Image Velocimetry (PIV). PIV is generally applied to exhibit the magnitudes and vectors of particle velocities and afford exact values of velocities. Measurements using a PowerView 2D PIV system (TSI, Shoreview, MN) were conducted at the inclined pipe region 1.83 m downstream from the bend. The laser light sheet generated by the Laser Pulse Solo Mini Dual Nd:YAG laser was introduced from the top of the wall/sidewall to lighten the granules at the center plane (labeled as “12” in Figure 1). Images of the granules were captured by a PowerView 4M (2K × 2K) camera in the

The method of combining the discrete element method (DEM) with CFD is well-established in the literature for numerical studies of various types of solid-fluid systems. Recently, it has also been applied successfully to reproduce the various flow regimes observed in pneumatic conveying of granular materials through vertical and horizontal pipes.11 Lim and co-workers12 have also described, in detail, a method of incorporating an electrostatic force model into the CFD-DEM model for numerical studies of pneumatic conveying processes with electrostatic effects. It was shown that the eroding dunes regime observed in previous experimental studies using inclined pneumatic conveying pipes could be reproduced computationally. Reversed flow of particles was observed in a dense region close to the bottom wall of the conveying pipe and forward flow in a more dilute region in the space above. The same methodology has been applied in the present study to complement the experimental investigations conducted. A brief outline of the main component of the CFD-DEM model is provided in the following section. 3.1. Discrete Element Method. The translational and rotational motions of individual solid particles are governed by Newton’s laws of motion: N dvi mi ) (fc,ij + fd,ij) + mig + ff,i + fE,i dt j)1

∑

dωi Ii

dt

(7)

N

)

Tij ∑ j)1

(8)

where mi and Vi are the mass and velocity of particle i, respectively; N is the number of particles in contact with this particle; fc,ij and fd,ij are the contact and viscous contact damping forces, respectively; ff,i is the fluid drag force due to an interstitial fluid; fE,i is the electrostatic force; Ii is the moment of inertia of particle i; ωi is its angular velocity; and Tij is the torque arising from contact forces, which will cause the particle to rotate. Contact and viscous contact damping forces must be calculated using force-displacement models, which relate such forces to the relative positions, velocities, and angular velocities of the colliding particles. In the present work, the linear forcedisplacement model was implemented for the calculation of


these collision forces. The normal (fcn,ij, fdn,ij) and tangential (fct,ij, fdt,ij) components of the contact and damping forces are calculated according to the following equations:

fcn,ij ) -κn,iδn,ij

(9)

fct,ij ) -κt,iδt,ij

(10)

fdn,ij ) -ηn,i (Vr‚ni)ni

(11)

fdt,ij ) -ηt,i (Vr‚ti)ti + (ωi × Ri - ωj × Rj)

(12)

where fcn,ij, fdn,ij and fct,ij, fdt,ij are the normal and tangential components of the contact and viscous contact damping forces, respectively; κn,i, δn,ij, ni, ηn,i and κt,i, δt,ij, ti, ηt,i are the spring constants, displacements between particles, unit vectors, and viscous contact damping coefficients in the normal and tangential directions, respectively; Vr is the relative velocity between particles; and Ri and Rj are the radius vector (from particle center to a contact point) for particles i and j, respectively. If |fct,ij| > |fcn,ij| tan φ, then “slippage” between the two contacting surfaces is simulated by a Coulomb-type friction law,

|fct,ij| ) |fcn,ij| tan φ where tan φ is analogous to the coefficient of friction. 3.2. Fluid Drag Force. In a multiphase system such as the gas-solid pneumatic conveying system considered in this study, interactions between the two phases take the form of fluid drag forces on the solid particles exerted by the interstitial fluid and arise from velocity differences between the two phases. In this study, the model due to Di Felice,13 which is applicable over a wide range of particle Reynolds numbers, was used to evaluate the fluid drag force:

where u is the velocity vector, the local average porosity, P the fluid pressure, and F the source term due to fluid-particle interaction. The computational domain was divided into uniform grid cells, and all quantities such as velocities and pressure were assumed constant over each cell. The source term F for a particular computational cell was calculated by summing the fluid drag forces on all particles present within that cell: n

F)

ff,i )

(13)

ff0,i ) 0.5cd0,iFf πRi2i2|ui - Vi|(ui - Vi)

[

]

(1.5 - log10 Rep,i)2 χ ) 3.7 - 0.65 exp 2

fE,i ) fEp,i + fEw,i

(

cd0,i ) 0.63 + Rep,i )

4.8 Rep,i0.5

)

2

2Ff Rii|ui - Vi| µf

(16)

(17)

∂ + ∇‚(u) ) 0 ∂t

fEp,i )

∑ j)1 j*i

Q2 4πorij2

(18)

∂(Ff u) + ∇‚(Ff uu) ) -∇P + ∇‚(µf ∇u) + Ff g - F ∂t (19)

ni

(22)

where Q is the constant charge assumed to be carried by all particles, o the permittivity of free space, rij the distance between particles i and j, and ni the unit normal vector in the direction of the line joining the two particle centers. In the present work, a dimensionless quantity Λ depicting the ratio of the electrostatic force arising from the charged pipe wall to the gravitational force exerted on each particle, fEw,i/ mig, is defined. In other words,

fEw,i ) Λmi g

where ff0,i is the fluid drag force on particle i in the absence of other particles, χ is an empirical parameter, i is the local average porosity in the vicinity of particle i, cd0,i is the drag coefficient, Rep,i is the Reynolds number based on particle diameter, Ff is the fluid density, µf is the fluid viscosity, and ui is the fluid velocity of the computational cell in which particle i is located. 3.3. Computational Fluid Dynamics. The motion of the continuum gas phase is governed by the Navier-Stokes equations with an additional source term in the momentum equation to represent the reaction force acting on the fluid by the particles:

(21)

where fEp,i and fEw,i are the electrostatic forces due to other charged particles and the pipe walls acting on particle i, respectively. The electrostatic force arising from charges carried by other particles may be calculated by assuming each particle to be a constant point charge:

(14) (15)

(20)

∆V

where ∆V is the volume of a computational cell and n is the number of particles present in the cell. 3.4. Electrostatic Effects. During pneumatic conveying, solid particles gain electrostatic charges as a result of repeated collisions and impacts against other particles and with the walls of the conveying pipe. The total electrostatic force acting on each particle may then be written as the sum of electrostatic forces due to charges carried by other particles and the pipe walls:

N

ff0,i-(χ+1) i

ff,i ∑ i)1

(23)

4. Results and Discussion 4.1. Flow Patterns and Velocities for Particle Transport in a 45° Inclined Conveying Pipe. Depending on the different air flow rates, three distinct phenomenasnamely, dispersed flow, reverse flow, and half-ring flowsfor particle transport in a 45° inclined conveying pipe was observed and schematically illustrated in Figures 2a, 2b, and 2c, respectively. When the air flow rate is high, particle flow is dilute and particles move in the direction of gas flow as shown in Figure 2a, the dispersed flow pattern. When air flow rate is decreased, some particles near the pipe center moved forward, while most of the particles formed layers at the bottom of the pipe and slid downward, which is called reverse flow (shown in Figure 2b). When the air flow rate was further decreased, particles formed a layer on the pipe wall, which resulted in an annular structure. This flow pattern is called half-ring flow (shown in Figure 2c). An

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Figure 2. Schematic of particle flow in three different flow patterns in pneumatic conveying: (a) dispersed flow; (b) reverse flow; and (c) half-ring flow, Panel (d) shows unsteady reverse flow with pulsating wave.

interesting unsteady flow patternsreverse flow with pulsating wave on the surfacesis also discussed in section 4.2.4. 4.1.1. Dispersed Flow Pattern. Figure 3 shows the images of particles concentration captured by ECT on plane 1 and plane 2, respectively. When the air flow rate is 1600 L/min, the particle concentration is generally low and particles do not concentrate on the pipe wall. As such, it forms the dispersed flow pattern. Figure 4 shows the result of velocity calculated by the bestcorrelated pixel method proposed by Mosorov and colleagues.10 The Mosorov method is modified from the classical crosscorrelation method (section 2.2) but is not limited by the basic assumption of the latter that the solid’s motion between the sensors is parallel to the pipe axis and perpendicular to the sensor plane. This method is to calculate cross-correlation between a pixel from the first plane and a number of pixels from the second plane. Therefore, the essential difference between the classical cross-correlation method and the best-correlated pixel method is the choice of pixels in the second plane. In the former, only corresponding pixels are correlated; however, in the latter, the

pixels from the second plane are chosen from the corresponding pixel and those in its neighbors (not just the nearest neighbors). Equation 24 describes the function in detail:

c(x,y,i,j,d) )

1 T

∫0T (R(x,y,z1,t) - Rt(x,y,z1))(R(i,j,z2,t + d) Rt(i,j,z2)) dt (24)

where (i,j) are dimensionless coordinates of the pixel in plane 2, R(x,y,z1,t) and R(i,j,z2,t + d) are the values associated with pixel (x,y) from the image at time t obtained from plane 1 and pixel (i,j) from the image at time (t + d) obtained separately from plane 2. Therefore, similar to the classical cross-correlation method, when c(x,y,i,j,d) reaches its maximum, d is D(x,y) and, according to eq 6, the axial solid velocity of each pixel, Vz(x,y), can be obtained. It is observed that velocities are high over the entire pipe (see Figure 4). Furthermore, the coordinates (i, j) on plane 2 (nondimensionalized by the pipe diameter as the characteristic length scale)


Figure 3. Images of particle concentration (R) at twin planes captured by ECT for the dispersed-flow pattern (air flow rate ) 1600 L/min).

The lateral velocity can be defined as the projection of B V on the pipe cross section and is described as

Vl(x,y) )

Figure 4. Particle axial velocity on pipe cross-section correlated from ECT data for the dispersed-flow pattern (air flow rate ) 1600 L/min).

can be obtained, according to the best-correlated pixel method. If i ) x, j ) y, it shows that the particles maintain their direction during the transport from plane 1 to plane 2; otherwise, it reflects the direction change of particles. Therefore, in such case, the actual velocity for particle transport between planes 1 and plane 2 is

()

Vx B V ) Vy Vz

(25)

Here, Vx, Vy, and Vz are the magnitudes of the velocity components in the three perpendicular directions, respectively.

2Rx(x - i)2 + (y - j)2 D(x,y)

(26)

where R is the pipe radius. The average lateral velocity for the dispersed flow pattern was calculated to be ∼8 × 10-4 m/s and appeared negligible, as compared to the axial velocity, as will be shown in Figure 6. Figure 5 shows the images of particle transport captured by a high-speed video camera (FastCam PCI, Photron, CA) at a frame rate of 250 fps. The motion of particles through the section of the conveying pipe could be visualized in slow motion after all the required frames were captured with the high-speed video camera. During this process, each particle could be tracked unambiguously from one frame to another, because the average distance traveled by each particle in the time interval between two consecutive frames was less than the diameter of the particle. This also allowed a specific particle to be identified in any two frames that are not necessarily consecutive to each other, such as those presented in Figure 5. The inclined pipes are positioned with the pipe axis at an angle of 45° relative to the direction of gravity, as indicated in Figure 5. The direction of air flow is from right to left. Similar illustration is also applied later to Figures 7 and 11. In Figure 5a, most particles are transported in regions close to the bottom pipe wall and the overall space among particles is fairly large, thus resulting in a dilute solid phase. For illustration purpose, one particle was chosen as an example and traced over several images. The positions of this particle in two images are marked in circles, as shown in Figure 5a. Generally, particle motion is observed to follow the gas flow direction. Subsequently, 10 particles were chosen randomly from 1000 pictures over a period of 4 s and

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Figure 5. Images of particle transport captured by a high-speed video camera: (a) dispersed flow (time interval between two successive pictures ) 0.008 s, air flow rate ) 1600 L/min); (b) reverse flow (time interval between two successive pictures ) 0.072 s, air flow rate ) 1100 L/min); (c) half-ring flow (time interval between two successive pictures ) 0.096 s, air flow rate ) 1000 L/min); (d) reverse flow with pulsating wave (time interval between two successive pictures ) 0.176 s, air flow rate ) 1100 L/min, PP with an antistatic agent).

the average velocity of particles was computed as the distance between the two positions in selected images divided by the duration between these two images. The average particle velocity value obtained was 1.59 ( 0.41 m/s. Figure 6 displays the velocity profile of particles at different positions along the pipe diameter. The data were obtained from ECT and PIV experiments, respectively. The figure shows that velocity profiles obtained from these two different methodologies exhibited similar trends. However, there are some quantitative differences, probably because of the different extents of experimental errors associated with the two instruments. Here, velocities are normalized with respect to the maximum value of velocity observed within the pipe cross section. The normalized velocities are high near the pipe center but decrease toward the pipe wall. Such profile was observed in both side view (Figure 6a) and top view (Figure 6b). This was also predicted by CFD simulation of pneumatic conveying of granular solids in an inclined pipe.3 It may also be observed from the velocity profiles in both side and top views in Figure 6 that lateral velocities are much lower than those of axial velocities, implying that axial movement is primary for such flow pattern, thereby validating the results obtained by eq 26 from the ECT data. Figure 7 shows the side view image from the top to the bottom of the pipe of the dispersed flow pattern captured by PIV, where the vector arrows verify the observation that the particle flow directions are consistent with the air flow.

4.1.2. Reverse Flow Pattern. When the air flow rate is decreased to 1100 L/min, it is observed in the experiment that some particles near or above the pipe center moved forward with fairly high velocities, whereas most particles were deposited and formed layers at the bottom of the pipe. These slid backward in a direction opposite to that of the general flow direction at relatively slow velocities. These are represented by the red areas in Figure 8. Figure 9 presents the resulting velocity obtained with the bestcorrelated pixel method for the reverse-flow pattern. In this figure, the entire solid phase is divided into three parts. It is observed that velocities are relatively high and positive near and above the center of the pipe, where the corresponding coordinate along the y-axis are 0.35-1, whereas those at the bottom (y ) 0-0.18) are very small and negative. These two areas are defined as dilute and dense regions, respectively. Particles at the interface between these regions (referenced as the transition region with y ) 0.18-0.35) flowed backward with relatively higher negative velocities. The lateral velocities calculated from eq 26 also show three distinct velocity scales, increasing from 10-6 m/s, to 10-5 m/s, to 10-4 m/s, from the dense region to the dilute region, respectively. The limitation of the cross-correlation method is that it is difficult to get exact values when data are the same on two correlation planes, because the principle of correlation is based on variation of the data on two planes. For the dense region, the concentrations of particles measured by two ECT sensors


Figure 7. Velocity vectors for the dispersed-flow pattern by PIV measurements (air flow rate ) 1600 L/min).

Figure 6. Diametrical distribution of particle axial velocity for the dispersed-flow pattern (air flow rate ) 1600 L/min): (a) side view and (b) top view.

are at the maximum values continuously. As a result, the velocities in this section are obtained from the images captured by a high-speed video camera, as shown in Figure 5b. It can be observed that most of granules are accumulated at the bottom of the pipe; however, a small amount is transported in the core region and at the top of the pipe. This is consistent with the solid fraction profile shown in Figure 8. In the dense region, particles at the bottom of the pipe seem almost stationary and the velocity obtained is only about -0.0020 ( 0.00072 m/s. The path traced by the particle is not shown, because it is not easily interpolated between the two images. In the transition region, some particles close to the core of the pipe are active and are referenced as transition particles. This is probably due to the shearing effects between the dilute and dense regions. The locations of the particle labeled with the symbol “A” in the three images indicate that it did not move ahead. Instead, it seemed to have jumped over some particles in a direction opposite to the air flow. The average velocity is -0.05 ( 0.02 m/s. However, in the dilute region, particles such as that labeled as “B”, moved ahead, with an average velocity of 0.62 ( 0.26 m/s. Correspondingly, the normalized particle velocity profiles obtained from both ECT and PIV and presented in Figure 10 demonstrate that three regions exist in the solid phase. Positive velocities in the dilute region are generally forward flow. In contrast, in the dense and transition region, negative velocities indicate reverse flow. In particular, the change in velocity profile

within the transition region revealed that reverse flow is significant in this zone. Figure 10 also shows that lateral velocities are much weaker in the dilute region, as compared to axial velocities, and, hence, can be neglected. However, in the transition and dense regions, the magnitudes of lateral and axial velocities are observed to be comparable. These findings further verify the three levels of lateral velocities observed from ECT data. Arrows in the vector plot of Figure 11 are pointing toward two completely opposite directions. This finding demonstrates that some particles are floating in the dilute region and moving forward, but some particles, especially those in the transition region, exhibit a backflow behavior. From the magnified zone, particles in the transition and dense regions also resulted in some wave structures in the transverse direction. 4.1.3. Half-ring Flow Pattern. When the air flow rate is further reduced to 1000 L/min, particles deposit at the bottom of the pipe and are stagnant initially. Later, particles concentrated on the pipe wall and gradually formed an annulus structure, while those at the bottom continued to remain stagnant, as shown in Figure 12. The thickness of this ring is roughly one layer of particles, and the solid concentration at the top of the pipe seems to be smaller than that at the bottom, because of the action of gravity. Figure 13 shows that velocity is zero at the bottom and relatively high at the top of the pipe wall, presenting an incomplete ring structure in the pipe cross-section. Correspondingly, the lateral velocities calculated according to eq 26 for the dense and dilute regions have magnitudes of 10-4 and 10-3 m/s, respectively. This shows that lateral motion is not negligible in the dilute region, while transverse motion becomes dominant in the dense region.

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Figure 8. Images of particle concentration (R) at twin planes captured by ECT for the reverse flow (air flow rate ) 1100 L/min).

Figure 9. Particle axial velocity on pipe cross-section correlated from ECT data for the reverse-flow pattern (air flow rate ) 1100 L/min).

Figure 5c shows that there is half-ring formation around the pipe wall. The ring of particles seemed to be suspended in the air or moving with lateral velocities. From the interspaces among the particles adhered on the pipe, it is observed that a small quantity of particles in the pipe core still moved ahead in the dilute region, and the average velocity is estimated to be 0.23 ( 0.06 m/s, using the previous method (particle B only moved a short distance during a time interval of 0.096 s). On the other hand, in the dense region, some particles settled on the bottom of the pipe (for instance, particle A appears almost motionless in the three frames). Because of the peculiar nature of the half-ring flow pattern, normalized particle velocity distributions near the pipe surface

and in the core region of the pipe are presented separately in Figure 14. This is shown in the sketch map of the pipe crosssection (Figure 2c), where both types of data are obtained from the correlation result from ECT measurements. From the surface velocity profile, it may be seen that the corresponding calculated velocity data points fall on the zero axes, demonstrating the stagnant ring flow, except that some positive values near the top indicate a small amount of forward flow in this area. As for the inner core region, combined with the measurement from high-speed video camera, the velocities at the bottom of the pipe are zero, because of the stagnant ring structure in the dense region. Some peak values indicated forward motion of a few particles in the dilute core region. Furthermore, a hollow core area around the center of the pipe is observed, emphasizing the existence of the half-ring structure. However, it may be noted at this point that velocity measurements using PIV is difficult for this particular type of flow pattern, because of blockage of the laser sheet from the system by particles adhered on the pipe walls. Because of the relatively large size of the particles used throughout this study, images of particles could be captured by the PIV camera, as long as the particles were slightly illuminated by the laser. In the dispersed- and reverse-flow regimes, the laser from the PIV systems was able to penetrate through the relatively dilute layer of solid particles near the pipe walls to illuminate those near the center of the conveying pipe. As such, particle velocities near the pipe center could be obtained. On the other hand, the solid concentration near the pipe walls was very high in the ring-flow regime and the PIV laser was completely blocked by this layer of particles near the walls. Thus, the particle velocity profile was unavailable for this flow regime. To validate the reliability of the various methods applied for velocity measurements in this study, the values of axial velocity for the three flow patterns measured by the three different


Figure 10. Diametrical distribution of particle axial velocity for the reverse flow (air flow rate ) 1100 L/min).

many anomalous behaviors in granular flow systems. It is believed that the formation of the various flow patterns described previously in pneumatic conveying through inclined pipes is related to electrostatic charge generation resulting from friction, collision, or rolling between particles and the pipe walls during the conveying process. To investigate the relationship between electrostatic effects and flow behaviors, the electrostatic charge generation characteristics for each of the aforementioned flow patterns will be discussed in the following sections. 4.2.1. Electrostatic Characters for Three Flow Patterns. In a previous work,6 electrostatic characteristics for three flow patterns have been studied by measuring the induced current on the pipe wall using an electrometer, when granular polypropylene (PP) were transported in horizontal and vertical pneumatic conveying pipes (made of PVC). Accordingly, the charge accumulated on the pipe wall can be calculated from eq 27:

q)

∫0T I dt

(27)

where I is the induced current measured from the electrometer and T is the time period. Recently, Yao et al.14 proposed the concepts of electrostatic equilibrium and averaged current:

hI )

Figure 11. Velocity vectors for the reverse-flow pattern from PIV measurements (air flow rate ) 1100 L/min).

methods are listed in Table 2. The velocities in the dense regions are fairly similar; however, in the dilute regions, data obtained via ECT and PIV seemed to contain a larger amount of noise and, thus, a wider range of values may be observed. 4.2. Electrostatic and Dynamic Analysis for Three Flow Patterns. Generally, electrostatic effects are responsible for

1 T

∫0T I dt

(28)

In their opinion, the averaged current fluctuated before reaching a constant value over a period of time (namely, the charging time, Tc). The periods where fluctuations occur and a steady value is reached are called the charging and electrostatic equilibrium states, respectively. After the state of electrostatic equilibrium is attained, the amount of charge residing on the particles and the pipe wall would remain more or less constant with time. The procedure of exploring whether the average current achieves electrostatic equilibrium has been specified in a previous study by Yao et al.14 An equilibrium state was deemed to have been attained when the ratio of variation in

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Figure 12. Images of particle concentration (R) at twin planes captured by ECT for the half-ring flow (air flow rate ) 1000 L/min).

reached are calculated for each of the three flow patterns, according to eq 27, by substituting T with the charging time Tc, and the results are listed in Table 3. 4.2.2. Simplified Electrostatic Field. A simplified electrostatic field12 is selected to describe a two-dimensional transverse section of pipe wall in accord with the numerical work and to perform the electrostatic analysis in this section. In comparison with the axial characteristic length scale of the pipe, the particle is sufficiently small such that charges on the pipe wall may be taken to be uniformly distributed. The charges on the wall are assumed to be infinitesimal point charges, dq, and every particle is taken as a point charge Q (assumption 1). By integrating the point charges over the entire wall, the electric field intensity due to charged pipe wall may be represented as follows:

E) Figure 13. Particle axial velocity on pipe cross-section correlated from ECT data for the half-ring-flow pattern (air flow rate ) 1000 L/min).

average current to the average current at the final state was 90%, thus verifying the adequacy of using Tc as an indication of the establishment of a state of electrostatic equilibrium. Therefore, the amount of charge accumulated on the pipe wall when equilibrium is

λ 1 dq ) ∫ 4π ∫π/2 cos θ dθ ) 2πλ 0l 2 2π0l 0 0 r

(29)

Here, 0 is the permittivity constant (8.85 × 10-12 C2/(N m2) under vacuum); q is the total equilibrium charge on pipe wall obtained from integration of the induced current, by eq 27; λ is the linear charge density along pipe wall, which is defined as the equilibrium charge on the pipe divided by the length of induced current measurement; r is the distance from a point charge on the pipe (dq) to a point charge (i.e., a charged particle) (Q); l is the vertical distance from the pipe wall to a point charge (i.e., a charged particle); and θ is the angle between r and l. 4.2.3. Dynamic Analysis for Single Particle on Pipe Wall. In the aforementioned model for dynamic force analysis, electrostatic interactions between particles were not taken into consideration (assumption 2). This assumption has been verified in a previous experimental study,14 where the electrostatic forces exerted on each particle by other particles due to the pipe wall were determined to be 1000) FgDp|u bg - b u p| µg

(31) (32) (33)

where µg is the gas viscosity, and b ug and b up are the translational velocity vectors of the gas and particle, respectively. (ii) Electrostatic force is assumed to be mainly contributed by the lower pipe wall in this simplified model, FE:

FE ) EQ

(34)

where Q is the electrical charge on each particle and can be obtained from multiplying the charge-mass ratio (charge density)6 by the mass of a single particle. (iii) Friction between particle and pipe wall: the product of normal force and coefficient of friction, which is estimated to be ∼0.56 from an internal angle of friction experiment.16 Table 3 displays the comparison of forces on a single particle for three flow patterns, where the particle velocity shown is the averaged value obtained from a high-speed video camera. For the dispersed-flow pattern, the magnitude of the electrostatic force, on average, is only 10-6 N and, thus, can be neglected; whereas the calculated aerodynamic drag force is more than 4 times and 300 times that of gravity and electrostatic force, respectively, showing that the primary driving force is indeed the drag force, which is also responsible for transporting the particles upward. For the reverse-flow pattern, the aerodynamic drag force in the dilute region was more than 10-4 N. This is still the dominant force, as compared to gravity and electrostatic forces. This implies that particles would also move upward in this region. In the dense region, aerodynamic drag force decreased

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Figure 15. Averaged current on pipe wall for three flow patterns (AF ) air flow rate; Tc ) charging time). Table 3. Comparison of Forces on a Single Particle for Three Flow Patterns Disperse Flow

Reverse Flow

parameter

average flow region

dilute flow region

air flow rate (L/min) particle velocity, b upa (m/s) equilibrium charge on the pipe, qb (C) charge per particle, Qc (C) gravity (N) drag force, B FDd (N) electrostatic force, FEe (N) friction on the bottom of the pipe (N) FD:G:FE

1600 1.6 -3.8 × 10-8 1.6 × 10-11 1.3 × 10-4 6.2 × 10-4 1.8 × 10-6 N.A. 345:71:1

1100 6.2 × 10-1 -1.0 × 10-6 2.6 × 10-11 1.3 × 10-4 5.0 × 10-4 8.0 × 10-5 N.A. 6.2:1.6:1

Half-ring Flow

transition flow region

dense flow region

-5.4 × 10-2

-2.0 × 10-3

4.1 × 10-4 2.3 × 10-4 N.A. 3.1:1:1.8

2.5 × 10-4 1.2 × 10-3 6.9 × 10-4 2.0:1:9.1

dilute low region 1000 2.3 × 10-1 -7.1 × 10-7 3.0 × 10-11 1.3 × 10-4 4.3 × 10-4 6.5 × 10-5 N.A. 6.6:1.9:1

dense flow region 0

2.1 × 10-4 9.3 × 10-4 5.7 × 10-4 1.6:1:7.4

a Particle velocity (u bp) is the averaged value and obtained from a high-speed camera. b Equilibrium charge on pipe (q) is calculated from eq 27, where T is the charging time Tc. c Charge per particle (Q) is obtained from multiplying the charge density by the mass of a single particle. d Drag force (F BD) is calculated from eq 30, where cD ) 0.44. e Electrostatic force (FE) is calculated from eq 34.

to the same range as gravity and could not provide enough driving force to transport particles upward, so that particles are likely to slide downward, because of the pull of gravity. However, the extents of electrostatic force and associated friction were high (∼10-3 N). It is probable that the electrostatic force causes particles to stick to the pipe wall and friction limits the reverse speed to almost zero. However, in the transition region, the magnitudes of the three types of forces were almost in the same ranges, indicating that particles should move either upward or downward. Some particles may be attracted and approach the dense region by electrostatic force. These particles are close to, but do not touch, the pipe wall and flow reversely; however, the reverse velocities in this region were greater than that of the bottom particles, because of the absence of friction for such suspended particles. Therefore, in this region, the track of particle motion was more wavelike, as shown in Figure 2b. On the other hand, some particles may still move ahead but also may collide with particles moving in the opposite direction, thus resulting in such particles turning around. Generally, the results

seem to confirm that the reverse-flow pattern is most significant in the transition region. In addition, the formation of a transition zone may be interpreted to indicate the presence of shearing instabilities at the interface between the dilute and dense regions. Particles in the dilute region move at higher velocities than those in the dense region. This relative velocity between the two regions causes significant shearing effects in a transition region between the two. Particles in this transition region are more unstable than those in the dense region. Furthermore, in the transition region, aerodynamic drag forces are smaller than those in the dilute region and electrostatic forces are smaller than those in the dense region. This resulted in the particularly negative velocities of solids within the transition region observed in the present study. Similarly, according to the report by Goldfarb et al.,17 a transition region formed at the interface between a steady state and a wavy state formed by two shearing granular flows in their experiment involving two streams of identical grains flowing on an inclined chute downstream of a splitter plate.


Figure 16. Comparison of electrostatic characters on the bottom of the pipe and the top of the pipe for the half-ring-flow pattern (air flow rate ) 1000 L/min): (a) induced current measurement section, (b) averaged current on the pipe wall, and (c) wall charge from integration of the induced current. Table 4. Electrostatic Forces on Single Particle in the Entire Reverse Area of Inclined Pneumatic Conveying (Air Flow Rate ) 1100 L/min) Value

a

parameter

PP without Larostat-519

PP with Larostat-519

particle velocity (m/s) equilibrium charge on pipe (C) charge per particle (C) electrostatic force (N) friction on the bottom of pipe (N) measured Λ valuea

10-2)-(-2.0

(-3.3 × 10-1)-(-1.7 × 10-1) -5.2 × 10-8 3.0 × 10-12 1.3 × 10-6-6.7 × 10-6 5.35 × 10-5 0.01-0.05

(-5.4 × × -1.0 × 10-6 2.6 × 10-11 2.3 × 10-4-1.2 × 10-3 6.9 × 10-4 1.8-9

10-3)

Λ ) FE/G.

As for the half-ring-flow pattern, the ratio of the three types of forces and the observations in the two regions were both similar to those of the reverse-flow pattern. As such, the details of the analysis will not be repeated here. Furthermore, particle velocity was much lower, because of a smaller air flow rate in the dilute region and particles had a tendency to remain stationary and form a ring structure on the pipe wall in the dense region and part of the dilute region, probably because of the force balance described previously; thus, the ring structure here was relatively stable during the entire transport process. In addition, a further experiment was performed to clarify the reason why a ring or half-ring structure formed. This

measurement is modified from the induced current test and is shown in Figure 16a, where the test section is divided into two parts and the experimental data can be obtained from the top and bottom of the pipe, respectively. The results of average currents calculated from eq 28 were shown in Figure 16b, in which equilibrium times, i.e., charging times (Tc) can be read as fairly similar values for two cases. Consequently, the induced currents were integrated with time to obtain the charge on the pipe wall (Figure 16c), according to eq 27. It is observed that the wall charge at the top of the pipe is greater than that at the bottom of the pipe during the entire experiment, as well as at the moment of equilibrium time. Therefore, the magnitude of

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Figure 17. Results of reverse-flow pattern with pulsating wave (air flow rate ) 1100 L/min): (a) normalized signal from two pressure transducers against time (4 s); (b) particle concentration (R) captured from two ECT planes against time (4 s); (c) power spectral density of ECT data in plane 1; and (d) power spectral density of ECT data in plane 2.

electrostatic force at the top of the pipe is high (up to 10-3 N); thus, such a value would be large enough to overcome the gravity and attract particles to stick on the upper part of the pipe wall. 4.2.4. Validation of Control Experiments. The unique feature of the reverse-flow phenomena, especially the velocity difference between the transition and dense region, is attributed to the electrostatic effect, as analyzed previously. Thus, it is anticipated that particles at the bottom of the pipe would slide downward with higher speed and, thus, the transition region would disappear, when the electric force was reduced. To verify this postulation, control experiments, which isolate the electrostatic effect on a system by holding constant all variables but

the one under observation, were performed. A commercially available antistatic agent, Larostat-519 powder,18 has been demonstrated to be a suitable means to reduce electrostatic effects effectively in a pneumatic conveying system.6 Larostat519 is a non-inflammable white powder with a bulk density of 520 kg/m3; it is composed of ∼60% soyadimethylethyl ammonium and ∼40% ethasulfate amorphous silica. In this experiment, 0.5% (by weight) of Larostat-519 powder was mixed with PP granules and other conditions were fixed to be the same as those for reverse flow. In comparison with previous cases, where no such agent was used, the equilibrium charge on the pipe wall and on each particle obtained in the presence of the Larostat-519 powder was smaller, by ∼2 orders of


Figure 18. ECT images of particle concentration (R) at test plane 2 when the air flow rate is 1000 L/min: (a) PP without an antistatic agent and (b) PP with an antistatic agent (Larostat-519 powder).

magnitude and 1 order of magnitude, respectively, as shown in Table 4. Correspondingly, a drastic drop in electric force acting on each particle at the bottom of the pipe, as well as frictional forces, were observed. Under the same air flow rate (1100 L/min), such small aerodynamic drag force cannot afford enough power to move particles upward, as mentioned in the last section. Consequently, particles on the bottom of the pipe slid downward with higher velocities, compared to the situation without an antistatic agent, because the small electric force and associated friction would not restrict particles in this region. Furthermore, bottom particles would drive other particles in the dense region with almost the same velocities. Thus, particles in the entire dense region flowed in the reverse direction. This process was captured by a high-speed video camera, as shown in Figure 5d. The range of the dilute region in these three images is basically the same as that in Figure 5b; however, no obvious transition region is observed. This is because particles A on the bottom of the pipe and particle B at the interface of the dense and dilute regions are moving with almost the same speed (-0.25 ( 0.078 m/s). Furthermore, during the experimental process of reverse-flow pattern without the influence of electrostatic forces achieved

by adding the antistatic agent, it was observed that particles did not slide downward in a smooth and steady manner. Instead, from the observation made in the present study, the speed of the reversing particles showed periodic fluctuations and solids moved downward in alternating pulses of high and low concentration, as shown in Figure 2d. The slow motion captured by the high-speed video camera presented this phenomenon in detail: initially, a stream of solids flowed down at a relatively high speed from downstream to upstream along the conveying pipe; then, the reverse speed of some particles decreased; these particles blocked those flowing back from downstream and accumulated on the upstream side of the pipe wall, making the solids stream intermittent. (This continued until friction between the particles and the wall or among the particles was unable to support the gravity of the group of particles.) The process was then repeated. In conclusion, the behavior of solids motion in the dense region exhibits a pulsating type of movement. Such flow pattern can be identified by the pressure fluctuations in the conveying of solids.19 Therefore, an additional measurement was performed to obtain the pressure data using two pressure transducers (Gems 2200BGA1002A3UA, Basingstoke, England) at distances of

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Table 5. Material Properties and System Parameters for CFD-DEM Simulations parameter

value/comment

shape of particles type of particles number of particles particle diameter particle density spring constant, κ coefficient of restitution coefficient of friction gas density gas viscosity pipe diameter pipe length pipe inclination computational cell size simulation time step, ∆t

spherical polypropylene, PP 1000 2.80 mm 1123 kg/m3 5.0 × 103 N/m 0.9 0.3 1.205 kg/m3 1.8 × 10-5 N s/m2 40.0 mm 1.0 m 45° 4 mm × 4 mm 10-7 s

0.85 and 1.85 m from the bend, respectively as labeled “16” and “17” in Figure 1. The pressure data were acquired simultaneously for 100 s with the sampling rate set at 100 Hz. Figure 17 shows the results of the normalized signal from the two pressure transducers against time (4 s). It is observed that two pressure waveforms from the two sensors are out of phase with each other, with each signal having a regular period of ∼1 s. The time lag (∆t) between the two waves indicated the time taken for one cluster of particles to slide from test point 1 to test point 2. The average ∆t value was obtained statistically to be 0.5 ( 0.3 s. The corresponding time lag between two particle concentration waves measured by two sets of ECT sensors was also observed to be similar in magnitude (see Figure 17b). The power spectral densities for both waves were obtained by a fast Fourier transform (FFT) of the pressure and concentration data, to have a more quantitative comparison of the dominant frequencies for both waveforms.

Figures 17c and 17d show that both power spectral density profiles exhibit a dominant peak at ∼1 Hz. This is also consistent with the fluctuation period of 1 s, as observed from Figures 17a and 17b. Another experiment was performed for the purposes of comparison and confirmation, by mixing an antistatic agent into particles at a fixed air flow rate of 1000 L/min. The ring-flow pattern then disappeared, as shown in Figure 18. 4.2.5. Validation of Numerical Results. To verify the aforementioned analysis, the experimental results for reverse flow were compared with a numerical simulation of pneumatic conveying of granular solids through a 45° inclined pipe, which was achieved using a simple electrostatic field model and DEM coupled with CFD. The geometry of the pneumatic conveying system and the type of particles used in the simulations are based on the experimental work. Material properties and system parameters are listed in Table 5. The number of particles used was 1000, corresponding to an overall solid concentration of β ) 0.16, where β is defined as the overall volume fraction of particles divided by the volume fraction of particles at maximum packing, which is generally taken to be 0.64. A dimensionless quantity (Λ) that indicates the ratio of electrostatic force arising from the charged pipe wall to the gravitational force acting on each particle is defined in section 3.4. The specific values used for the various parameters, such as the spring constant and coefficients of restitution and friction, have been shown to have minimal effects on the flow patterns produced from the CFDDEM simulations in a sensitivity analysis performed by Lim et al.11 In all simulations performed, particles were first allowed to settle freely under gravity for 0.5 s and form a packing at the “bottom” of the pipe before gas flow was initiated. Periodic boundary conditions were applied to the solid phase to simulate an open flow system while a uniform gas velocity profile was maintained at the inlet. Particles that were carried out of the

Figure 19. Numerical result of reverse flow [β ) 0.16 (1000 particles)]: (a) enlarged image of one section in pneumatic conveying through a pipe (inlet gas velocity ) 10 m/s, Λ ) 5.0) and(b) diametrical distribution of particle axial velocity.


conveying pipe by the flowing gas were simulated to re-enter from the inlet of the pipe with the same velocities and radial positions. Figure 19a successfully shows that reverse-flow behavior can be observed in particles moving along the bottom wall, when the inlet gas velocity is 10 m/s and Λ ) 5.0. Figure 19b describes the solid velocity distributions along the pipe diameter from the bottom of the pipe (y ) 0) to the top of the pipe (y ) 1). Here, particle velocities are actual values and not normalized, to have a good comparison between the two groups of data. In this figure, the symbols at the bottom right-hand corner represent the inlet gas velocities and the dimensionless quantity Λ. Consequently, when electrostatic force was 5 times the magnitude of the gravitational force (Λ ) 5), negative velocities appeared. This shows that some solids at the bottom of the pipe may move in a direction opposite to the air flow. In particular, a peak negative value (-0.48 m/s) in the velocity between the positions y ) 0.2 and y ) 0.3 corresponds to the transition region and illustrates a quantitative agreement with the experimental data (-0.077 m/s to -0.031 m/s). However, when the electrostatic force was absent (Λ ) 0), the velocity profile showed more significant backflow (-0.55 m/s to -0.38 m/s) in the dense region. Furthermore, the change from negative values to positive values from the bottom to the top of the pipe indicates the gradual disappearance of the transition region. Therefore, these results demonstrate that the electrostatic force is an essential determinant of negative solid velocities in the transition zone of the reverse-flow regime. Generally, the simulation results show good agreement with the experimental results and physical observations. 5. Conclusions The concentration distribution of polypropylene (PP) particles transported in a 45° inclined pneumatic conveying pipe was measured using electrical capacitance tomography (ECT). By applying the best-correlated pixel method, the characteristics of velocities and directions of particle motions in three different flow patterns were described and compared with results of particle image velocimetry (PIV) and high-speed video camera measurements. It is concluded that when the air flow rate is high, the entire solid phase is dilute and particles are dispersed over the entire cross section of the pipe with high velocity, especially in the pipe center. In contrast, at low air flow rates, most of the solid particles are deposited at the bottom of the pipe and some of them are transported in the upper part of the pipeline, forming the dense and dilute regions, respectively; the corresponding velocity distribution shows the presence of reverse flow in a transition region between these two regions. The reverse-flow pattern is also observed in the computational fluid dynamics-discrete element method (CFD-DEM) simulation results. When the air flow rate is decreased further, a halfring flow structure is formed and the majority of particles adhered to the pipe wall. The major forces acting on single particles were analyzed for the three flow patterns, including the drag force, electrostatic force, gravity, and friction. For the dispersed-flow pattern, the dilute region of the reverse-flow pattern, and the half-ring-flow pattern, aerodynamic drag force was the major driving force transporting particles upward. For the dense region of the reverse-flow pattern and half-ringflow pattern, the electrostatic force predominated and attracted particles onto the pipe wall. For the transition region of reverse flow, three major forces were in the same ranges and caused particles to be in a suspended state. In this region, particles would be drawn by the gravitational force to flow

downward. Thus, the electrostatic force was essential for the occurrence of three regions in reverse flow, and this was also validated by the control experiments and the results of CFDDEM simulation. Acknowledgment This study has been supported by the SERC (A*STAR), under Grant No. R-279-000-208-305. The authors are grateful to Dr. Jun Yao, Dr. Kewu Zhu, Fong Yew Leong, and Lai Yeng Lee for many helpful discussions on this project. Literature Cited (1) Levy, A.; Mooney, T.; Marjanovic, P.; Mason, D. J. A comparison of analytical and numerical models with experimental data for gas-solid flow through a straight pipe at different inclinations. Powder Technol. 1997, 93, 253-260. (2) Hirota, M.; Sogo, Y.; Marutani, T.; Suzuki, M. Effect of mechanical properties of powder on pneumatic conveying in inclined pipe. Powder Technol. 2002, 122, 150-155. (3) Zhu, K;, Wong, C. K.; Rao, S. M.; Wang, C. H. Pneumatic conveying of granular solids in horizontal and inclined pipes. AIChE J. 2004, 50, 17291745. (4) Zhu, K.; Rao, S. M.; Wang, C. H.; Sundaresan, S. Electrical capacitance tomography measurement on vertical and inclined pneumatic conveying of granular solids. Chem. Eng. Sci. 2003, 58, 4225-4245. (5) Mare´, T.; Voicu, I.; Miriel, J. Numerical and experimental visualization of reverse flow in an inclined isothermal tube. Exp. Therm. Fluid Sci. 2005, 30, 9-15. (6) Yao, J.; Zhang, Y.; Wang, C. H.; Matsusaka, S.; Masuda, H. Electrostatics of the granular flow in a pneumatic conveying system. Ind. Eng. Chem. Res. 2004, 43, 7181-7199. (7) Rao, S. M.; Zhu, K. W.; Wang, C. H.; Sundaresan, S. Electrical capacitance tomography measurements on the pneumatic conveying of solids. Ind. Eng. Chem. Res. 2001, 40, 4216-4226. (8) Su, B. L.; Zhang, Y. H.; Peng, L. H.; Yao, D. Y.; Zhang, B. F. The use of simultaneous iterative reconstruction technique for electrical capacitance tomography. Chem. Eng. J. 2000, 77, 37-41. (9) Hua, J. S.; Wang, C. H. Electrical capacitance tomography measurements of gravity driven granular flows. Ind. Eng. Chem. Res. 1999, 38, 621-630. (10) Msosorov, V.; Sankowski, D.; Manzurkiewicz, L.; Dyakowski, T. The ‘best-correlated pixels’ method for solid mass flow measurements using electrical capacitance tomography. Meas. Sci. Technol. 2002, 13, 18101814. (11) Lim, E. W. C.; Wang, C. H.; Yu, A. B. Discrete element simulation for pneumatic conveying of granular material. AIChE J. 2006, 52, 496509. (12) Lim, E. W. C.; Zhang, Y.; Wang, C. H. Effects of an electrostatic field in pneumatic conveying of granular materials through inclined and vertical pipes. Chem. Eng. Sci. 2006, 61, 7889-7908. (13) Di, Felice, R. The voidage function for fluid-particle interaction systems. Int J. Multiphase Flow 1994, 20, 153-159. (14) Yao, J.; Zhang, Y.; Wang, H, C.; Liang, Y. C. On the Electrostatic Equilibrium of Granular Flow in Pneumatic Conveying Systems. AIChE J. 2006, 52, 3775-3793. (15) Sommerfeld, M. Analysis of collision effects for turbulent gasparticle flow in a horizontal channel: Part I. particle transport. Int. J. Multiphase Flow 2003, 29, 675-699. (16) Zhang, Y.; Wang, C. H. Particle Attrition due to Rotary Valve Feeder in a Pneumatic Conveying System: Electrostatics and Mechanical Characteristics. Can. J. Chem. Eng. 2006, 84, 663-679. (17) Goldfarb, D. J.; Glasser, B. J.; Shinbrot, T. Shear instabilities in granular flow. Nature 2002, 415, 302-305. (18) Zhang, Y. F.; Yang, Y.; Arastoopour, H. Electrostatic effect on the flow behavior of a dilute gas/cohesive particle flow system. AIChE J. 1996, 42, 1590-1599. (19) Dhodapkar, S. V.; Klinzing, G. E. Pressure fluctuations in pneumatic conveying systems. Powder Technol. 1993, 74, 179-195.

ReceiVed for reView October 12, 2006 ReVised manuscript receiVed March 23, 2007 Accepted March 30, 2007 IE061304I

Pneumatic Transport of Granular Materials in an Inclined Conveying

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